Tensor Squeezed Limits and the Higuchi Bound

TL;DR

Tensor consistency relations for primordial perturbations are remarkably robust, persisting even in multi-field scenarios as long as long-wavelength tensor modes act as adiabatic backgrounds and anisotropies dilute like $a^{-1}$; the Higuchi bound reinforces this by forbidding light spin-2 fields in (approximately) de Sitter space. Violations, possible in models with broken de Sitter isometries such as Solid Inflation, would signal persistent anisotropic hair and non-adiabatic tensor modes, with observable imprints including a graviton-exchange contribution to the scalar trispectrum and a quadrupolar modulation of the scalar power spectrum. The authors quantify how these effects could be detected via the CMB and large-scale structure, showing that the key observable is the combination $f_{\rm NL}^{\gamma 2} r$, and they propose dedicated analyses of the scalar four-point function and quadrupole statistics to distinguish tensor-induced features from a privileged direction. Overall, detecting or constraining tensor CR violations offers a powerful window into the isotropization dynamics of inflation and the possible presence of additional spin-2 degrees of freedom. $${}$

Abstract

We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor con- sistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) Graviton exchange contribution to the scalar four-point function; (b) Quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.